# Refer to Exercise 5.66. If F1(y1) and F2(y2) are two distribution functions then for any

## Problem 5.163 Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Problem 5.163

Refer to Exercise 5.66. If F1(y1) and F2(y2) are two distribution functions then for any , 1 1, F(y1, y2) = F1(y1)F2(y2)[1 {1 F1(y1)}{1 F2(y2)}] is a joint distribution function such that Y1 and Y2 have marginal distribution functions F1(y1) and F2(y2), respectively. a If F1(y1) and F2(y2) are both distribution functions associated with exponentially distributed random variables with mean 1, show that the joint density function of Y1 and Y2 is the one given in Exercise 5.162. b If F1(y1) and F2(y2) are both distribution functions associated with uniform (0, 1) random variables, for any , 1 1, evaluate F(y1, y2). c Find the joint density functions associated with the distribution functions that you found in part (b). d Give two specific and different joint densities such that the marginal distributions of Y1 and Y2 are both uniform on the interval (0, 1).

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Refer to Exercise 5.66. If F1(y1) and F2(y2) are two distribution functions then for any

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